Andreas M. Köster

Density functional theory optimized basis sets for gradient corrected functionals: 3d transition metal systems

Density functional theory optimized basis sets for gradient corrected functionals for 3d transition metal atoms are presented. Double zeta valence polarization and triple zeta valence polarization basis sets are optimized with the PW86 functional. The performance of the newly optimized basis sets is tested in atomic and molecular calculations. Excitation energies of 3d transition metal atoms, as well as electronic configurations, structural parameters, dissociation energies, and harmonic vibrational frequencies of a large number of molecules containing 3d transition metal elements, are presented. The obtained results are compared with available experimental data as well as with other theoretical data from the literature.

Structure and stability of small copper clusters

The structure and stability of small copper clusters with up to ten atoms has been determined both for the neutral and the ionic clusters with density functional calculations. The calculations were of all-electron type. The structure optimization and frequency analysis were performed on the local density approximation level with the exchange correlation functional by Vosko, Wilk, and Nusair. Subsequently improved calculations for the stability were based on the generalized gradient approximation, where the exchange correlation functional of Perdew and Wang was used. Finally, the binding energies, ionization potentials, electron affinities, and separation energies were calculated. The results show that the trends are in agreement with available experimental data.

Calculation of exchange-correlation potentials with auxiliary function densities

The use of Hermite Gaussian auxiliary function densities from the variational fitting of the Coulomb potential for the calculation of exchange-correlation potentials is discussed. The basic working equations for the energy and gradient calculation are derived. The accuracy of this approximation for optimized structure parameters and bond energies are analyzed. It is shown that the quality of the approximation can be systematically improved by enlarging the auxiliary function set. Average errors of 0.5 kcal/mol are obtained with auxiliary function sets including f and g functions. The timings for a series of alkenes demonstrate a substantial performance improvement.

An adaptive numerical integrator for molecular integrals

We present a new numerical integrator for molecular integrals that generates automatically an adaptive molecular grid. The tolerance of the numerical integration is the only input parameter of the integrator besides the atomic coordinates and the atomic numbers. The adaptive numerical integrator was successfully implemented in our new density-functional theory method (DFT method) ALLCHEM using the self consistent field (SCF) procedure. The accuracy of the numerical integration is superior to pruned fixed grids for a given number of grid points. The adaptive grid generator allows a very efficient optimization of the grid for an individual molecular system. It is shown that the grid accuracy increases monotonically, if the given tolerance of the numerical integration is decreased. In this way it is possible to obtain results of high numerical precision. For a given tolerance of the numerical integration the adaptive grid generator automatically adjusts the grid to the basis set and the molecular structure. ...

Efficient and reliable numerical integration of exchange-correlation energies and potentials

An adaptive numerical integrator for the exchange-correlation energy and potential is presented. It uses the diagonal elements of the exchange-correlation potential matrix as a grid generating function. The only input parameter is the requested grid tolerance. In combination with a defined cell function the adaptive grid generation scales almost linear with the number of basis functions in a system. With the adaptive numerical integrator the self-consistent field energy error, which is due to the numerical integration of the exchange-correlation energy, converges with increasing adaptive grid size to a reference value. The performance of the adaptive numerical integration is analyzed using molecules with first, second, and third row elements. Especially for transition metal systems the adaptive numerical integrator shows considerably improved performance and reliability.

Density functional calculations of molecular polarizabilities and hyperpolarizabilities

This paper presents dipole moments, static polarizabilities, first hyperpolarizabilities and second hyperpolarizabilities calculated in the framework of density functional theory. All calculations have been performed using a finite field approach implemented in our new density functional theory program ALLCHEM. The calculations were of all-electron type. Both local and gradient-corrected functionals have been used. The influence of first- and second-order field-induced polarization functions, the external field strength, the numerical integration technique and the exchange-correlation functionals on the calculation of polarizabilities and hyperpolarizabilities is discussed in detail. A systematic study including 23 small and medium size molecules demonstrates that the obtained polarizabilities as well as the first and second hyperpolarizabilities are in good qualitative agreement with experimental data. The described density functional method provides polarizabilities and hyperpolarizabilities considerabl...

A density functional study of small copper clusters: Cun (n⩽5)

Density functional calculations have been performed for small copper clusters, Cun (n≤5), using the linear combination of Gaussian‐type orbitals density functional theory (LCGTO‐DFT) approach. The calculations were of the all‐electron type and local and nonlocal functionals were used. For each case, of both neutral and charged systems, several isomers have been considered in order to determine the lowest energy structures. The Jahn–Teller effect in Cu3 and Cu4 has been examined in detail. Bond lengths, equilibrium geometries, harmonic frequencies, adiabatic and vertical ionization potentials, adiabatic electron affinities, and binding energies are in reasonable agreement with experimental data, as well as with other theoretical results.

Geometry optimization in density functional methods.

The geometry optimization in delocalized internal coordinates is discussed within the framework of the density functional theory program deMon. A new algorithm for the selection of primitive coordinates according to their contribution to the nonredundant coordinate space is presented. With this new selection algorithm the excessive increase in computational time and the deterioration of the performance of the geometry optimization for floppy molecules and systems with high average coordination numbers is avoided. A new step selection based on the Cartesian geometry change is introduced. It combines the trust radius and line search method. The structure of the new geometry optimizer is described. The influence of the SCF convergence criteria and the grid accuracy on the geometry optimization are discussed. A performance analysis of the new geometry optimizer using different start Hessian matrices, basis sets and grid accuracies is given.

Hermite Gaussian auxiliary functions for the variational fitting of the Coulomb potential in density functional methods

The use of primitive Hermite Gaussian auxiliary functions for the variational fitting of the Coulomb potential is discussed. Integral recurrence relations for three-center electron repulsion integrals and integral sums with these auxiliary functions are derived. An asymptotic expansion of three-center electron repulsion integrals with primitive Hermite Gaussian auxiliary functions is presented. The recurrence relations for the asymptotic expanded integrals are given. Integral pathway diagrams and density matrix assignment diagrams are presented for all target integrals. The calculations of the three-center electron repulsion integrals of alkenes indicate that the new algorithms represent a substantial performance improvement.

Topological analysis of the molecular electrostatic potential

The topology of the molecular electrostatic potential of 18 molecules, calculated in the framework of Kohn–Sham density functional theory, is studied. For the location of the different kinds of critical points a newly developed search algorithm is applied. A chemical interpretation of the critical points in terms of lone pairs, π bonds, hybrid orbitals and other electronic structure elements is suggested. A Poincare–Hopf relationship for the molecular electrostatic potential is derived, connecting electronic structure elements and electrostatic reactivity via the topology of the molecular electrostatic potential.